12
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Number sequence puzzles are very popular of late.</sarcasm>

Therefore, I present to you another one. I promise you it has no relation to any sequence in OEIS, nor will it ever be found there, and it does not require any mathematics at all to be solved. It is also not based on a language.

What are the next numbers in the following sequence?

1, 2, 7, 12, 13, 16, 18, 19, 20, ...

Hint 1:

The sequence will always be finite, but it grows every day.

Hint 2:

Every one of you has seen some elements of this sequence.

Hint 3:

There is a related sequence which contains most (but not all) numbers not appearing in this sequence. It starts with 4, 5, 6, 8, 14, 15, 21, 23, 24, ...

Hint 4:

I have made some contributions to this list, but only a handful. The person contributing the most has over 200 entries.

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  • $\begingroup$ The answer is obviously 42 and 42, because duh. $\endgroup$ – Xenocacia Jan 6 '17 at 1:06
  • $\begingroup$ "The sequence will always be finite, but it grows every day." could refer to population or the universe. $\endgroup$ – Oliver Ni Jan 8 '17 at 19:20
3
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My shot.

Next numbers : 22, 25, 27, ... these are the post numbers from Puzzling SE that are questions.

Here is part of the list:

1: Are there "rules" (or consistent conventions) that limit when the NY Times Crossword can deviate from rotational symmetry?
2: What is the maximum number of solutions a Sudoku puzzle can have?
7: How many queens can be on a chessboard without attacking each other?
You can find the rest yourselves.

Hint 1:

The sequence will always be finite, but it grows every day.
Each day there are questions added to this website but there will never be an infinite number of questions.

Hint 2:

Every one of you has seen some elements of this sequence.
Everyone on this website has seen at least one question. (Thanks OP for showing me I cannot read properly :D )

Hint 3:

There is a related sequence which contains most (but not all) numbers not appearing in this sequence. It starts with 4, 5, 6, 8, 14, 15, 21, 23, 24, ...
On SO websites, the ids for questions and answers are shared.
So some of the ids are not questions.
4: What is the maximum number of solutions a Sudoku puzzle can have?
5: What is the maximum number of solutions a Sudoku puzzle can have?
This answers sequence does not contain the rest of the numbers because some of them have been deleted.

Hint 4:

I have made some contributions to this list, but only a handful. The person contributing the most has over 200 entries.
The OP has 3 contributions to the list at the time I'm writing this. SO 3 questions.
But the person who contributed to the list of questions is Gamow and he has 201 questions at the time when this answer is written.
You can see that he is the user with the most questions in here

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  • $\begingroup$ This is the correct solution; hint 2 refers to (rot13) gur nqqerff one bs lbhe oebjfre. $\endgroup$ – Glorfindel Jan 10 '17 at 9:47
  • $\begingroup$ Right...I misread something. I will change it. Thanks $\endgroup$ – Marius Jan 10 '17 at 9:49
6
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The sequence continues as

22 and 24,

because

the numbers in the sequence form an exact match to Eric Prinsen's performance results he achieved during a pigeon-flying competition at station Rethel in 2016.

Regarding the hints hidden in the surrounding text:

It is highly unlikely that such a short, finite sequence will ever correspond to anything mathematically interesting, therefore I don't think it will be part of the OEIS in the foreseeable future.

If this is your personal achievement, then I warmly congratulate to your awesome results! No sarcasm intended, and no pigeons were harmed during the preparation of this answer.

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  • 2
    $\begingroup$ The hint says that the sequence "grows every day". Is that compatible with this answer? (It doesn't seem like it.) $\endgroup$ – Gareth McCaughan Jan 6 '17 at 0:44
  • $\begingroup$ Wow ... well found, but not the intended solution. It is indeed not satisfying the "grows every day" hint. $\endgroup$ – Glorfindel Jan 6 '17 at 8:38
  • $\begingroup$ In fact, it's the first thing that appears on Google if you search for "1, 2, 7, 12, 13, 16, 18, 19, 20". $\endgroup$ – IAmInPLS Jan 6 '17 at 11:11

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